MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f1(Ar_0, Ar_1, Fresh_7, Fresh_8, Fresh_9, Ar_5, Ar_6, Ar_7)) [ Fresh_8 >= 1 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f1(Ar_0, Ar_1, Fresh_4, Fresh_5, Fresh_6, Ar_5, Ar_6, Ar_7)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f1(Ar_0, Ar_1, Fresh_3, 0, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f300(Ar_0, Ar_1, Fresh_1, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0, Fresh_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Fresh_8 >= 1 /\ Ar_0 >= Ar_1 + 1 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) (Comp: 1, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Fresh_8 >= 1 /\ Ar_0 >= Ar_1 + 1 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.586 sec (SMT: 0.547 sec)